Question

A Cincinnati marketing firm specializes in assessments of local restaurants and have been asked to rate Wilmington's local restaurants. The restaurants are rated as good, fair, or poor. From the firm's rating system, 72% of the restaurants were rated good, 20% of the time rated poor, and the remainder were rated fair. Of those rated good, 80% made a profit in the 1st year, 65% of those rated fair made a profit in the 1st year and 45% of those rated poor made a profit in the 1st year.

a) What is the overall probability that a Wilmington restaurant made a profit in the first year?

b) What is the likelihood that a randomly selected restaurant that made a profit in the first year that was rated poor by the marketing firm?

Please show you work.

Answer 1

a)

overall probability that a Wilmington restaurant made a profit in the first year

=P( rated good and mad profit)+P( rated fair and mad profit)+P( rated poor and mad profit)

=0.72*0.8+0.08*0.65+0.2*0.45=0.718

b)

P(poor given made profit)=P( rated poor and mad profit)/P(made profit)

=0.2*0.45/0.718=0.1253